相关论文: Rest Frame System for Asymptotically Flat Spacetim…

We report a new result on the nice section construction used in the definition of rest frame systems in general relativity. This construction is needed in the study of non trivial gravitational radiating systems. We prove existence,…

We prove the positive mass theorem for asymptotical flat (AF for short) manifolds with finitely many isolated conical singularities. We do not impose the spin condition. Instead we use the conformal blow up technique which dates back to…

We propose a definition of center of mass for asymptotically flat manifolds satisfying Regge-Teitelboim condition at infinity. This definition has a coordinate-free expression and natural properties. Furthermore, we prove that our…

There exists in General Relativity an unambiguous notion of Mass associated to asymptotically flat spacetimes known as the ADM mass. The standard expression for the same is a surface integral over spatial infinity of a linear combination of…

Asymptotically flat static causal fermion systems are introduced. Their total mass is defined as a limit of surface layer integrals which compare the measures describing the asymptotically flat spacetime and a vacuum spacetime near spatial…

The question of existence of general, asymptotically flat radiative spacetimes and examples of explicit classes of radiative solutions of Einstein's field equations are discussed in the light of some new developments. The examples are…

Away from the central axis, we prove the stability of the Positive Mass Theorem in the $W^{1,p}$ sense for asymptotically flat axisymmetric manifolds with nonnegative scalar curvature satisfying some additional technical assumptions. We…

The Nagumo lattice differential equation admits stationary solutions with arbitrary spatial period for sufficiently small diffusion rate. The continuation from the stationary solutions of the decoupled system (a system of isolated nodes) is…

We consider a family of cosmological models in which all mass is confined to a regular lattice of identical black holes. By exploiting the reflection symmetry about planes that bisect these lattices into identical halves, we are able to…

We consider a relativistic radiating spherical star in conformally flat spacetimes. In particular we study the junction condition relating the radial pressure to the heat flux at the boundary of the star which is a nonlinear partial…

The idea of monotonicity (or positive-definiteness in the linear case) is shown to be the central theme of the solution theories associated with problems of mathematical physics. A "grand unified" setting is surveyed covering a…

We show the existence of some infinite families of periodic solutions of the planar Newtonian n-body problem --with positive masses-- which are symmetric with respect to suitable actions of finite groups (under a strong--force assumption,…

We define the center of mass and spin of an isolated system in General Relativity. The resulting relationships between these variables and the total linear and angular momentum of the gravitational system are remarkably similar to their…

We present a method to determine the equilibrium geometry of large atomistic systems with linear scaling. It is based on a separate treatment of long and short wavelength components of the forces. While the rapidly varying part is handled…

On a smooth asymptotically flat Riemannian manifold with non-compact boundary, we prove a positive mass theorem for metrics which are only continuous across a compact hypersurface. As an application, we obtain a positive mass theorem on…

We prove the existence of static, asymptotically flat non-vacuum spacetimes with axial symmetry where the matter is modeled as a collisionless gas. The axially symmetric solutions of the resulting Einstein-Vlasov system are obtained via the…

This paper considers some the existence and uniqueness of strong solutions of stochastic neutral functional differential equations. The conditions on the neutral functional relax those commonly used to establish the existence and uniqueness…

In this article and its sequel we discuss the asymptotic structure of space-times representing isolated bodies in General Relativity. Such space-times are usually required to be asymptotically flat (AF), and thus to have a prescribed type…

We study central configurations when the set of positions is symmetric. We use a theorem from representation theory of finite groups to explore the symmetry properties of equations for central configurations. This approach simplifies…

An important concept in Physics is the notion of an isolated system. It is used in many different areas to describe the properties of a physical system which has been isolated from its environment. The interaction with the `outside' is then…